Successive approximation rotary angle to digital converter



Nov. 25, 1969 F. N. DI MEO 3,480,946

SUCCESSIVE APPROXIMATION ROTARY ANGLE T0 DIGITAL. CONVERTER Filed March 51, 1966 2 Sheets Sheet REF AMPUHER EXCLUSIVELY CLIPPER OR 75 INVERTER 73 B SINGN AMPLIFIER k74 CLIPPER t, 52 /53 {72 v 55 55 sme OUTPUTS I'OMULTIPLIER FG-2 BLOCKS R| cosqb 92 se FIG.3

INVENTOR FRANK N D MEO ATTORNEY United States Patent O 3,480,946 SUCCESSIVE APPROXIMATION ROTARY ANGLE TG DIGITAL CONVERTER Frank N. DiMeo, Philadelphia, Pa., assgnor to Ltton Precision Products, Inc., Clfton Heights, Pa., a corporation of' Delaware Filed Mar. 31, 1966, Sex. No. 539,060 Int. Cl. H041 3/00 U.S. Cl. 340-347 Claims ABSTRAC'I OF THE DISCLOSURE A rotary angle to digital convarter having a plurality of cascaded stages for succassively raducing an angular quadrant of the rotary angle to be determined and With each stage employing circuits tor subtracting fixed reference angles from the angle by trigonomatric identity processing.

The present inventon relates to analog to digital convarters and specifically to shaft angle to digital converters utilizing signals reprasentative of trigonometric functions of the angle.

Two types of devices have been used extansively to perform shaft to digital conversion, utilizing trigonometric functions. In ona type, sina and cosine functions are represented as series of pulsa trains which are generated by suitable transducers. These pulsa signals serva to control counters which follow the pulsa train signals and indicate the angular position of the shaft. Obviously, the equipment necessary to tranduce the angular motion to alectrical pulsa trains and the counters must be quite axpensive and complex in order to be reliable within any reasonable limits. Further, rapid variations in input angular motion necassitates a time delay sufficiant to anable the counters to respond stap by step to such changes. And, the time allowed for any reading must be suflicient to allow for the longest response.

In yat anothar type of shaft to digital converter, trigonometric functions are compared to reference signals by the linear approximation method. This method is inherently slow and inaccurata, and even slower and more inaccurate when operating on trigonometric funetions. Because the trigonometric function is not at all linear in certain regions, for example the sina function near 90, these regions must be aither axcluded completely from considaration, or at best, larga discrepancies will occur.

The present inventon provides a converter in which the need for linear successive approximation techniques, or counters and pulsa generators, is obviated by utilizing equipment which acts upon signals indicative of the trigonometric functions of the angular position of an input shaft. Very generally according to the inventon, analog signals reprasenting the sina and cosina of the angle to be encodad are successivaly diminished by analog refarance angle signals dacreasing in value of angle, by the use of trigonometric identities. A digital code is produced representing the various reference angles contained in the shaft angle to be encodad.

An object of the present inventon is the provision of an accurate and inexpensiva shaft to digital convertar.

A further object of the inventon is the provision of a raliable and rapid shaft to digital converter.

Yet a still further object is to provide for a lightweight convertar having a minimum number of components without sacrificing quality or accuracy of operation.

-Other objects and advantages of this inventon will become more fully apparant from consideration of the following description taken in conjunction with the accompanying drawing Wherein:

FIG. 1 illustrates in block diagram from one embodiment of the inventon;

FIG. 2 dapicts a block diagram of the comparator selector block of the embodiment of FIG. 1; and

FIG. 3 is a partial block, partial schematic diagram of a typical multiplier block of the convarter of FIG. 1.

Briefly, the converter operation comprises deriving an analog input signal reprasentative of the sina and cosine functions of an angle 0 through which an input shaft has moved, comparing the sina function to the sina of a refarence angle I deriving a digital output signal dependent upon the result of the comparison, and generating analog signals representative to the sin (lh) and cos (0-1P) which are applied to the next successive ancoder stage, where t,l/= I if t9 and 1//=0 if 6 Ix The next stage utilizes the same circuits as the previous stage, but employs a different and smaller reference angle function for comparison. The analog output function of this stage is supplied to a further stage using a still smaller reference angle With the total number of such stages being employed depending upon the accuracy of the output signal desired. By utilizing logie circuitry, which acts directly upon the values of trigonometric funetions and converts by utilizing well known trigonometric identities, the arror, created by the disparity present in prior art devices betwean linear approximations and the value of the function for any angle, is removad.

Turning now to FIG. 1 of the drawing, there is shown a rasolver 9 from which two output leads 51 and 52 connect to a first ancoder stage 11, the lead 51 splits to provide input signals to a comparator 12, and multipliers 13 and 16, whila output laad 52 provides connactions to multipliers 14 and 15. Comparator 12 has another input signal sin I applied thereto over lead 53, and provides output signals over leads 54 and 55. The laad 54 provides one bit of the output signal of the convertar which may connect to a storage or indicating device or to subsequent circuitry (net shown). The signal derived from comparator 12 over lead 55 is connected to aach of the multiplication devices 13 to 16. Multipliars 13 and 14, and 15 and 16 are connected to addition or sumrnation circuits 17 and 18 over laads 56 to 59, respectivaly. The outputs from summers 17 and 18 are applied as input signals to the next ancoder stage 21 over leads 61 and 62.

Encoder stages 21 to N are of identical structure and operation as ancoder stage 11, differing therefnom only in the input and raference function signals applied thereto.

Considaring the operation of this system in greater detail, the rasolver 9 is connected to an input shaft (not shown) which is rotated to an angle 0 from a referenca point. This shaft angle is that information which the device Will convert to digital information. The angle 0 is assumed to be acute. The quadrant of the angla may be generated as a digital quantity by any of a number of means Well known to those skilled in the art. The signals over leads 51 and 52 are representative of sin 0 and cos 0 raspectively. The amplitude of the sin 0 signal applied to comparator 12 is compared in comparator 12 with the amplitude of the raference signal sin I applied over lead 53. If sin 0 is equal to or graater than the sin in, the output from the comparator 12 over leads 54 will be a first signal level, for example, a binary 1. A second level of output signal, perhaps a binary 0, Will be generatad if sin 0 is less than the sin I The output over lead 54 serves as the first bit of the output signal. Zero or one signals may be generated if a binary output is desired or the output of each stage may be weighted to supply a counter or the like, so that another digital number base may be used.

The output over lead 55 is applied to each of the multipliers 13 to 16. Multipliers 13 and 15 serve to muitiply cos by sin 0 and cos 0 respectively and multipliers 14 and 16 serve to inultiply sin 1,b with cos 0 and sin 0 respectively. If the comparison produces a first level or sin 0,zsin I, then \//1=q on the other hand, if the second level is produced or sin 0 sin then 1/ =0.

Multiplier 13 produces a signal sin 9 cos l/ over lead 56, and multipiier 14 produces a signal cos 0 sin i// over lead 57. These sgnals are added or sumrned in circuit 17 and the output over lead 61 is: sin 0 cos P -cos 0 sin 1/ A well known trigonometric identity is that sin 0 cos 1// -cos 0 sin 1P1 Sin (fi -W). In a similar manner, the output of adder 18, appearing on lead 62 is: cos 0 cos x,h+sin 0, sin 1,b =cos (0 1 Setting 0 -z/ =6 the inputs to encoder stage 21 are sin 0 and cos 0 The same operation oceurs in stage 21 ielding the second output bit signal over lead 64 and signals equal to sin 0 and cos 0 serve as inputs to the next encoder stage. Where where N is equal to the order of the encoder stage. Thus the reference signal t0 stage 11 Will be sin 45.000, to stage 21, sin 22.500 to stage 31 sin 11.250 and to stage N Resolver 9 Will generate signals sin 60 and cos 60. A first level or binary 1 Will be generated by comparator 12 since sin 60 sin 45, and the signal over lead 55 Will be such that =45. Thus, the output of adder 17 Will be sin 15 or sin (60-45 and added 18 Will generate a signal cos 15. These last mentioned signals are applied to encoder stage 21 over leads 61 and 62. Since I =22.5 in this example, and 0 1 (15 22.5), a binary zero output signal will be generated by comparator 22 over leads 64 and 65 and b =0. Thus the outputs from summation circuits 27 and 28, sin 0 and cos 0 Will be sin 15 and cos 15.

The reference signal applied to the comparator of the third encoder stage N is or sin 11.25. Since 15 is greater than 11.25", a first level output is generated by the comparator in this stage and 1/ Will equal 11.25 The angle 0 sine and cosine functions of which are applied to the fourth stage, Wil be sin 5.6250 and cos 5.6250.

In succeeding stages if present, the same process occurs as has been described above in conjunction with the operation of stages 11, 21 and N. Thus, if N W6re equal to or there were 5 encoder stages, a binary indication of a shaft angle of 60 would appear as the code 10101. As generally mentioned above, the same digital output would be present for angles of 120, 240 and 300 and an additiona1 bit or bits would indicate which of the specific angles Was present.

Turning now to FIG. 2, a block diagram of the comparator and selector stages 12, 22, etc., there is shown a pair of amplifier-clipper blocks 71 and 72, the input to amplifier 71 being a suitable reference voltage and the input to amplifier 72 being the output of a summer or adder circuit 73. The inputs to comparator 73 being sin 0 and -sin over leads 51 and 53 (FIG. 1), respectiveiy. The output of amplifiers 71 and 72 designated A and B, are connected to an exclusive or circuit 74, the output of which is connected to the multipliers 13 to 15, et t' I 1 over 1@ d 55' an e erte p t e 4 1oad 55" via inverter 75. The leads 55' and 55" correspond to lead 55 shown in FIG. 1 as a single lead for the sake of simplicity.

In operation the signal sin 0 is compared to the signal representing sin in comparator or adder 73, the output of which is amplified and eiipped in a conventional manner in block 72 and the reference voltage is similarly amplified and clipped in block 71. Both of these signals are applied to the exclusive or gate 74.

The logie for an exclusive OR is that an output signel is generated if either input is applied thereto but not if both are applied. Hence the truth abie is:

A B F Since the reference voltage is always at a level after amplification and clipping (A) to produce a voltage suflicient to qualify as an input signal to gate 74, we need only consider the first two possibilites in the truth table. First, if sin 6 2sin I then a B signal qualifying as an input to gate 74 is produced yieiding an output from gate 74 of E this signal is inverted in block 75 and produces a signal level E However, if sin 0 sin I a negative comparison results, the B signal is not qualifying and an E output is generated by gate 74. The E output is inverted and appears as E on lead 55". Thus for the first condition voltages as shown are produced on leads 55' and 55", and for the second condition the voltages are interchanged.

A typical multiplier block, cos i,b is shown in FIG. 3, consisting of an input lead 51 via resistor to an operationai amplifier 81 having a first feedback loop 82 with a feedback resistor 83 in the loop and a second feedback loop 84 with a second feedback resistor 85 in the path. These loops are switched into feedback relationships in the circuit via suitable switches such as transistors 86 and 87 shown. The switches are controlled by connection to leads 55' and 55" from the comparator 12. The output leads 88 and 89 of the multiplier are surnrned in adder circuit 91.

In operation, with voltage E, on lead 55' and voltage E on lead 55" transistor 86 is conductive and transistor 87 is nonconductive. Because of the high input impedance and low output impedance of the device virtually all the input current flows through to lead 88. The impedance of resistor 85 is of such magnitude that virtually no current flows therethrough. Hence, as in a single feedback amplifier the output is equal to the input times the ratio of the value of resistor 83 over the value of input resistor 80. Assigning a value of R to resistor 80 and R cos I to resistor 83, knowing the input signal over lead 51 to be sin 0 the output signal is equal to:

sin 0 R If resistor 85 is in current, voltage E appearing on lead 55" and E on 55', rendering transistor switch 87 conductive and switch 86 nonconductive, the output appears as sin 0N sin 0 1 Thus as was shown above, if sin 0 2 sin I the output on lead 56 is sin 0,; cos I and if sin 0 sin q the output is sin 6 A multiplier block for a sin l/ function may be fabricated by replacing resistor 83 with a resistor having a value of R; sin 0 and resistor 85 with a short circuit.

Thorof0re, the outputs of multplior 14, for oxamplo would be os 1 R1 cos 6 s1n in and for the othor soloction Sinco the invontion rosides in the combination of circuit olomonts and not in any one particular olomont, all of which individually are woll known in the prior art, rocourso may be had to the litoraturo for a doscription of such elemonts. No nocessity Was seon for overburdening the spocificaton with a doscription of an embodimont ornploying specific circuitry. Suflico it to say that the goneral arrangoment, since oach of the stagos is substantially identical, roadily adapts to modular design utilizing statoof-tho-art micrologic or intogratod circuitry providing for a roliablo, lightwoight, shockproof, and low powor dovico.

Obviously, many modifications and variations of the present invontion are possiblo in light of that taught boreinboforo. It is thoreforo undorstood, that the invontion may be practicod Within the scope of the appondod claims, otherwiso, thon as spocifically doscribod.

What is claimod is:

1. In a shaft anglo to digital convortor, a plurality of cascadod encodor stages, oach having moans for cornparing analog signals roprosontativo of a trigonomotric function of a first anglo to a signal roprosontativo of a trigonornotric function of a roforonco anglo, means for providing a first digital output signal in responso to said comparison, moans oporativoly connoctod to said last montionod moans for gonorating a pair of simultanoous analog output signals ropresentativo of a pair of trigonomotric identity functions of the difforonco betwoen said first anglo and said roforonco anglo if said first anglo is at least equa] to said roforonco anglo and for gonorating sgnals roprosontativo of said first anglo if said anglo is loss than said roforonco anglo, and moans for applying said pair of analog output signals to the next oncodor stage for obtaining the noxt digital output.

2. In the convorter of claim 1, said genorating moans including a plurality of multipliors oporativoly connoctod to said comparison moans and a plurality of addors operativoly connoctod to said multipliors.

3. In the convortor of claim 1, further moans for providing input signals to the first of said stagos indicative of trigonomotric functions of an angular position to bo convortod and means for operativoly coupling the signals from said genorating moans of a procoding stage to the comparison and gonorating means of a succeoding stage.

4. The dovice of claim 3 whoroin said functions are sino and cosine functions.

5. The dovco of claim 3 whoron oach of said generating means includos first and socond multipliors to which are applied signals represontative of the sino functon and third and fourth multipliors to Which are applied signals roprosontativo of tho cosine function, and first and socond addors oporativoly couplod to said first and third multipliors and said second and fourth multipliers, rospoctivoly.

6. Tho dovico of claim 3 whoroin said furthor moan is a rosolvor.

7. In the convorter of claim 6, said comparison -moans furthor including, means for goneratng the signal indicativo of said roforonco anglo whoro said anglo in any one stage is oqual to 45 2 whoro N is the ordor numbor of that particular stage.

8. A rotary anglo to digital convortor ccmprising:

aplurality of cascadod stagos,

moans producing a pair of analog signals roprosonting digoront trigonomotric functions of the rotary anglo. and applying said pair of analog signals to one of said cascadod stagos,

moans in said stage for comparing one of sai-d pair of analog signals with an analog reforonco signal corrosponding to the same trigonornotric function of a fixod roforonco anglo to produco a digital sign-al corresponding to the groator of the analog and roforonco signal,

moans rosponsivo to the digital signal whon the referonco sgnal is groator than the analog sgnal to transmit the pair of analog signals to the noxt stage and rosponsivo to the digital signal when the analog signal is groator than the roforonco signal to transmit a pair of socond analog signals to the next stage that are proportional to diiforont trigonomotric functions of the difforonco in anglo botwoen the rotary anglo and the roforonco anglo,

said moans for gonerating said pair 0f socond analog signals comprising a plurality of multiplying circuits and addor circuits rosponsivo to the pair of analog signals and to the roforonco sgnal to multiply the l'oforonco signal by oach Of the pair of analog signals and algebraically sun1 the products thoroby to provido said pair of socond analog signals corrosponding to difforont trigonomotric idontity functions of the analog signals and reforonco signals.

9. In the convortor of clairn 8, said moans for producing a pair of anal0g signals comprising moans for producing signals constituting the sino and cosino functions of the rotary anglo.

10. In the convertor of claim 8, said moans for gonerating the pair of socond analog signals comprising moans for applying one of said pair of analog signals and said roforonco signal to a first of said multiplying circuits to obtain a first product, moans for applying the othor of said analog signals and said roforonco signal to a second multiplying circuits to obtain a socond product, and moans for onorgizing said addor circuit by said pair of multplying circuits to algebraically sum said first and socond products.

References Cited UNITED STATES PATENTS 3,071,324 1/1963 Shroedor et al. 340-347 3,100,298 8/1963 Fluhr 340-347 3,188,624 6/1965 McMillian 340-374 3,357,012 12/1967 Brook 340-347 3,376,570 4/1968 Lawson 340-347 MAYNARD R. WILBUR, Primary Examiner MICHAEL K, WOLENSKY, Assistant Examinor 

